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2 years ago

The equation of a circle centered at the origin is x^2+y^2=16. what is the radius of the circle?

Mathematics

1 answer:

vekshin12 years ago

4 0

Answer:

The center is (0,0) and the radius is 4

Step-by-step explanation:

x^2+y^2=16.

The equation of a circle can be written in the form

(x-h)^2+(y-k)^2=r^2 where ( h,k) is the center and r is the radius

(x-0)^2+(y-0)^2=4^2

The center is (0,0) and the radius is 4

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What is the equation in point-slope form of a line that passes through the points (−4, −1) and (5, 7) ?

Sergio039 [100]

The point-slope form:

$y-y_1=m(x-x_1)$

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (-4, -1) and (5, 7). Substitute:

$m=\dfrac{7-(-1)}{5-(-4)}=\dfrac{7+1}{5+4}=\dfrac{8}{9}\\\\\boxed{y-7=\dfrac{8}{9}(x-5)}$

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2 years ago

A beverage company wanted to see if people in the United States liked their new logo. Which choice best represents a population?

olga55 [171]

Answer:

Every person in the US.

Step-by-step explanation:

If a selection of logo artists are asked whether they like or not the new logo, their answer will represent only the opinion of a specific group of artists of the US, and this is not the objective of the beverage company,who wants to know if people from the United States like their logo.

If 3,800 children age 5-15 are asked whether they like the logo or not, their opinion will only represent the opinion of some children in the US, whose age is between 5 and 15, and again, this is not the objective of the beverage company,who wants to know if people from the United States like their logo.
Finally, the population (which by definition includes all the elements under study, in this case, all the people in the US) will be defined by all people in the US: if the company wants to know if people from the US like their new logo, they must take into account that, the population under study is all people, and not a biased selection of it.

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3 years ago

Find a power series representation for the function. (Give your power series representation centered at x = 0.) f(x) = x/6x^2 +

timama [110]

Looks like your function is

$f(x)=\dfrac x{6x^2+1}$

Rewrite it as

$f(x)=\dfrac x{1-(-6x^2)}$

Recall that for $|x|$ , we have

$\dfrac1{1-x}=\displaystyle\sum_{n=0}^\infty x^n$

If we replace $x$ with $-6x^2$ , we get

$f(x)=\displaystyle x\sum_{n=0}^\infty\frac(-6x^2)^n=\sum_{n=0}^\infty (-6)^n x^{2n+1}$

By the ratio test, the series converges if

$\displaystyle\lim_{n\to\infty}\left|\frac{(-6)^{n+1} x^{2(n+1)+1}}{(-6)^n x^{2n+1}}\right|=6|x^2|\lim_{n\to\infty}1=6|x|^2$

Solving for $x$ gives the interval of convergence,

$|x|^2$

We can confirm that the interval is open by checking for convergence at the endpoints; we'd find that the resulting series diverge.

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2 years ago

What is an equation of the line that passes through the points (3, 0) and (6, -1)

Shalnov [3]

Y= -1/3x + 1

Please mark BRAINLEST!!

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2 years ago

Read 2 more answers

The ideal width of a safety belt strap for a certain automobile is 6 cm. The actual width can vary by at most 0.45 cm. Write an

OlgaM077 [116]

Answer:

$|x-6|\le 0.45$

$x\in [5.55,6.45]$

Step-by-step explanation:

Absolute Value Inequality

Assume the actual width of a safety belt strap for a certain automobile is x. We know the ideal width of the strap is 6 cm. This means the variation from the ideal width is x-6.

Note if x is less than 6, then the variation is negative. We usually don't care about the sign of the variation, just the number. That is why we need to use the absolute value function.

The variation (unsigned) from the ideal width is:

$|x-6|$